Prime p₀= 2167822258769119367 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 40 2 58 2 40 2 28 2 (?)
a_n: 0 2 30 32 72 74 132 134 174 176 204 206
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 206
Found by: Roadranner
db: batch=81, k=12, 2 28 2 40 2 58

SPT(16)	2167819955905196011	0 12 18 42 70 172 180 202 228 250 258 360 388 412 418 430	-2302863923356
STPT(10)	2167819963366195049	0 2 18 20 30 32 42 44 60 62	-2295402924318
SPT(16)	2167820378113567679	0 20 38 54 80 98 102 110 132 140 144 162 188 204 222 242	-1880655551688
STPT(10)	2167821273288131441	0 2 30 32 78 80 126 128 156 158	-985480987926
SPT(16)	2167821618087820549	0 10 52 78 82 84 138 144 148 154 208 210 214 240 282 292	-640681298818
SPT(16)	2167822011157387033	0 10 28 66 78 96 130 166 168 204 238 256 268 306 324 334	-247611732334
SPT(16)	2167822298165253707	0 80 84 96 110 174 186 204 206 224 236 300 314 326 330 410	39396134340
TPT(16)	2167822324534468409	0 2 108 110 168 170 300 302 318 320 330 332 348 350 372 374	65765349042
SPT(16)	2167822373632563749	0 8 14 50 62 84 110 122 150 162 188 210 222 258 264 272	114863444382
STPT(10)	2167822443197472179	0 2 18 20 30 32 42 44 60 62	184428352812
STPT(10)	2167822653453281171	0 2 6 8 48 50 90 92 96 98	394684161804